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The space of k linear continuous operators from X Polarization constants As a first step, desiguldades us introduce the polarization constants, which can be regarded as a particular case of the factor problem. We will treat separately the lower and the upper bound.

Make your selections below, then copy and paste the code below into your HTML source. In particular c h d.

### Jorge Tomás Rodríguez – Google 학술검색 서지정보

As a corollary from a result of [BST] it is easy to see that the best possible constant K n, for complex Banach spaces, is n n. The relative width of a plank is the width of the plank divided by the width of the convex body in the direction that the plank attains its width. In the particular case when X is a Hilbert space, due to poolinomiales symmetry of the sphere, desigkaldades may even expect that they are uniformly distributed across the sphere. On the next page click the “Add” button.

This, and the fact that the Mahler measure is multiplicative, makes it possible to deduce inequalities regarding the norm or the length of the product of polynomials using the Mahler measure as a tool. In order to do this we will work with measures satisfying a not too restrictive property. In Chapter 3 we study the factor problem on Banach spaces, considering the standard uniform norm for polynomials.

The factor problem is the problem of finding lower bounds for the norm of the product of polynomials polinomialees some prescribed degrees. In order to introduce the notion of polynomials on Banach spaces we start by 7. X R is an homogeneous polynomial.

## Rodríguez, Jorge Tomás

Upper bounds For the upper bounds we will obtain a slightly better result, since we will get upper bounds for c n X rather than for c x. In particular, in Functional Analysis, the study of multilinear forms and polynomials has been growing in the last decades. Remez type inequalities In this section, we introduce Remez type inequalities for polynomials.

Facultad de Ciencias Exactas y Naturales. K K For example, for H a Hilbert space, the Lebesgue measure over S H is admissible, since the functions g m are constant functions that converge to the constant function g. To add the widget to iGoogle, click here. This question remains unanswered in the general case, but for centrally symmetric convex bodies the solution was given by K.

Por su interminable paciencia y estar siempre presentes para aconsejarme y asistirme.

## DESIGUALDADES CON VALOR ABSOLUTO – Casos 2 y 3

Note that for a finite dimensional space K d,this definition agrees with the standard definition of a polynomial on several variables, where a mapping P: Given a Banach space X, we denote its topological dual by X, the norm on the space by X or, when it is clear from context.

In the previous proof we only use from the Definition. Definition Given k N, a mapping P: Although, as mentioned before, finding these linear functions is not an easy task, it seems reasonable to assume that these linear functions have to be spread out in S X.

Arens [Ar] generalized this to k linear operators and R. In particular we prove that for the Schatten classes the optimal constant is 1.

Aplicamos las cotas inferiores obtenidas para el producto de polinomios al estudio de este problema y obtenemos condiciones suficientes para espacios de Banach complejos. Polarization constants of l d p desiguwldades spaces In this section we apply the method developed in the previous section, stated in Theorem. C d C, P not identically zero, is the geometric mean of P over the d-dimensional torus T d with respect to the Lebesgue measure: The following is the main result of this section and gives the asymptotic behaviour of the polarization constants c l d p k as d goes to infinity.

These type of inequalities have been widely studied by several authors in a variety of contexts.